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Constancy of generalized Hodge–Tate weights of a local system
Published online by Cambridge University Press: 06 November 2018
Abstract
Sen attached to each $p$-adic Galois representation of a
$p$-adic field a multiset of numbers called generalized Hodge–Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a
$p$-adic local system on a rigid analytic variety over a
$p$-adic field and show that the multiset of generalized Hodge–Tate weights of the local system is constant. The proof uses the
$p$-adic Riemann–Hilbert correspondence by Liu and Zhu, a Sen–Fontaine decompletion theory in the relative setting, and the theory of formal connections. We also discuss basic properties of Hodge–Tate sheaves on a rigid analytic variety.
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- Research Article
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- © The Author 2018
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